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Modeling Coupled Evaporation and Seepage in Ventilated Tunnels
T. A.Ghezzehei *, R. C. Trautz, S. Finsterle, P. J. Cook, and C. F. Ahlers1
Earth Sciences Division Lawrence Berkeley National Laboratory University of California MS 90R1116, 1 Cyclotron Rd., Berkeley, CA 94720-8126
Manuscript submitted to Vadose Zone Journal (TOUGH special issue)
* Corresponding author, Tel (510) 486-5688, Fax (510) 486-5686, Email TAGhezzehei@lbl.gov
1 Now at LFR Levine Fricke, Costa Mesa, California
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
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ABSTRACT 1 Tunnels excavated in unsaturated geological formations are important to activities such 2
as nuclear waste disposal and mining. Such tunnels provide a unique setting for simultaneous 3
occurrence of seepage and evaporation. Previously, inverse numerical modeling of field liquid-4
release tests and associated seepage into tunnels were used to provide seepage-related large-scale 5
formation properties by ignoring the impact of evaporation. The applicability of such models was 6
limited to the narrow range of ventilation conditions under which the models were calibrated. 7
The objective of this study was to alleviate this limitation by incorporating evaporation into the 8
seepage models. We modeled evaporation as an isothermal vapor diffusion process. The semi-9
physical model accounts for the relative humidity, temperature, and ventilation conditions of the 10
tunnels. The evaporation boundary layer thickness (BLT) over which diffusion occurs was 11
estimated by calibration against free-water evaporation data collected inside the experimental 12
tunnels. The estimated values of BLT were 5 to 7 mm for the open underground tunnels and 20 13
mm for niches closed off by bulkheads. Compared to previous models that neglected the effect of 14
evaporation, this new approach showed significant improvement in capturing seepage 15
fluctuations into open tunnels of low relative humidity. At high relative- humidity values, the 16
effect of evaporation on seepage was very small. 17
18
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
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INTRODUCTION 18 Seepage of liquid water into tunnels is an important phenomenon for subsurface activities 19
such as mining and geologic disposal of nuclear wastes. A key factor affecting the long-term 20
safety of the proposed nuclear waste repository at Yucca Mountain (YM), Nevada, is the seepage 21
of liquid water into waste emplacement tunnels. The rate, chemical composition, and spatial and 22
temporal distributions of seepage are critical factors that determine corrosion of waste canisters, 23
integrity of engineered barriers, and dissolution and mobilization of contaminants and their 24
release to groundwater (Bodvarsson et al., 1999; Finsterle et al., 2003). In unsaturated 25
formations, capillary forces hold the pore water tightly in the formation and prevent it from 26
seeping by gravitational forces into the tunnel – the invisible barrier created by the capillary 27
force is commonly known as a “capillary barrier.” Philip and co-workers (Knight et al., 1989; 28
Philip, 1989a; Philip, 1989b; Philip et al., 1989a; Philip et al., 1989b) considered steady-state 29
unsaturated flow around capillary barriers and provided analytical solutions for the critical 30
conditions that trigger seepage into various idealized tunnel goemetries excavated in 31
homogeneous formations. Detailed numerical models have been used to study unsaturated flow 32
in heterogeneous fractured media and seepage into tunnels of various geometries under transient 33
conditions (e.g., Birkholzer et al., 1999; Finsterle, 2000; Finsterle and Trautz, 2001; Li and 34
Tsang, 2003). Site-specific seepage models for the nuclear waste repository at Yucca Mountain, 35
Nevada were developed by calibrating the effective seepage-related parameters against field 36
seepage test data (Finsterle et al., 2003). 37
Most of the previous numerical models assumed that liquid water leaking into a tunnel 38
drips (seeps) immediately at the place of entry. The potential for evaporation to compete with 39
seepage has been generally ignored, and its effect was lumped with the effective flow parameters 40
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
Page 4of 39
of the unsaturated medium (Finsterle et al., 2003). In calibration of the analytical model of Philip 41
et al. (1989b) against field seepage data, Trautz and Wang (2002) accounted for the effect of 42
evaporation by adjusting the field seepage data for evaporation. Because the data were obtained 43
from tests conducted in relatively humid tunnels, the effect of evaporation on the calibrated 44
seepage-related parameter was not significant. However, recent field measurements of seepage 45
and free-water evaporation in ventilated tunnels at Yucca Mountain have shown that seepage rate 46
is significantly influenced by evaporation. The foregoing discussions suggest that the 47
applicability of models that ignore evaporation is limited to similar humidity and temperature 48
conditions under which the calibrations are performed (Finsterle et al., 2003). Such models 49
cannot satisfactorily capture the seepage rate fluctuations when the seepage experiments are 50
conducted under variable humidity and ventilation conditions. More importantly, seepage models 51
that ignore evaporation, and that are calibrated against seepage data under ventilated and/or low 52
humidity conditions are not expected to perform well in predicting future seepage conditions that 53
are expected to be non-ventilated and humid. The preceding observations call for a calibrated 54
seepage model that reliably performs over a wide range of ventilation and humidity conditions. 55
The objective of this study is to improve the portability of calibrated seepage models by 56
reducing the impact of evaporation on the calibrated effective parameters. Thus, we propose to 57
incorporate evaporation from tunnel walls into the existing seepage models by assuming a first-58
order diffusion approximation. 59
EVAPORATION IN TUNNELS 60 Fundamentally, evaporation is a two-step process. The first step involves transition from 61
liquid to vapor phase at the liquid-vapor interface (vaporization). The second step is the transport 62
of vapor from the high concentration area at the evaporating surface to the low concentration 63
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
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area of the ambient air. Accurate modeling of these coupled processes is difficult for several 64
reasons: (1) the first step is a non isothermal phenomenon, and the parameters that govern this 65
process are strongly temperature dependent; (2) the vapor concentration gradient in the boundary 66
layer is strongly influenced by the air flow regime; and (3) the air flow depends on among other 67
things the ambient wind velocity and the roughness of the evaporating surface. 68
Ho (1997) and Or and Ghezzehei (2000) modeled evaporation from individual water 69
droplets attached to tunnel ceilings, assuming constant temperature and humidity conditions. 70
However, the scale of their approach is too small to be incorporated into the larger scale seepage 71
models that represent the discrete dripping process as a continuum flow. Therefore, the 72
evaporation model required in this study should be of an intermediate scale and be compatible 73
with the existing seepage models. The formulation used herein capitalizes on the observed 74
dependence of evaporation rate on tunnel humidity and ventilation conditions, and the 75
availability of high resolution time-series data of relative humidity, temperature and free-water 76
evaporation rate (Trautz and Wang, 2002). 77
In the following subsections, we introduce an isothermal vapor diffusion model of 78
evaporation and define the problem domain and boundary conditions. This is followed by 79
estimation of the evaporation model parameters, using free-water evaporation data. Finally, a 80
remark on evaporation from porous surface is provided. 81
Isothermal Vapor Diffusion Model 82 To simplify the first step of evaporation (vaporization) we assume the following: (1) the 83
absorption of latent heat and its effect on the physical properties of the liquid-vapor interface are 84
ignored; (2) the time dependence of the vaporization process (e.g., Zhang and Wang, 2002; 85
Zhang et al., 2001) is neglected; and (3) the vapor partial pressure of the interfacial air is 86
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
Page 6of 39
assumed to be under thermodynamic equilibrium. At equilibrium, the air above a flat surface of 87
pure water is considered saturated with vapor; its vapor pressure is denoted by sp . This 88
saturation vapor pressure rises with temperature. In the temperature range of –10°C to 50°C, the 89
saturation vapor pressure is related to interfacial temperature by (Murray, 1966): 90
cbT
Tap ++
=sln [1] 91
where 8721.=a , C5265 °= .b and 416.=c are constants, and T is the interfacial temperature. 92
For non-flat interfaces (such as capillary menisci) the actual interfacial vapor pressure p is 93
related to the interfacial capillary potential by the classic Kelvin equation, 94
TR
MPpp
W
WC ρ⋅=
sln [2] 95
where CP is the capillary pressure, Wρ and WM are the density and molecular mass of liquid 96
water, respectively, and R is the universal gas constant. Note that the relative humidity of air is 97
defined as the ratio of the actual partial pressure ( p ) to the saturated vapor pressure ( sp ) 98
spph = [3] 99
The second step of evaporation, vapor removal from the interface, is modeled as a first-100
order phenomena described by Fickian diffusion (Rohsenow and Choi, 1961). In one dimension 101
and under constant temperature, the vapor flux ( vJ ) is given by 102
zCDJ VTV d
d⋅−= [4] 103
where VD is the vapor diffusion coefficient, which is related to the ambient air pressure ( P ) and 104
air temperature (T ) by 105
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
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815
5
152731010132
.
..
×= −
TP
DV [5] 106
and the vapor concentration C is related to vapor pressure by 107
pTR
MC W ⋅= [6] 108
In the subsequent subsection, we define the problem domain and develop the appropriate 109
boundary conditions needed to solve the vapor diffusion equation [4]. 110
Velocity and Concentration Boundary Layers 111 In admitting diffusive flux as the primary mechanism for vapor removal from the 112
evaporating surface, we tacitly assume that airflow above the evaporating surface is fully 113
developed and laminar, as illustrated in Fig. 1a. The free-stream air velocity ( ∞V ) is retarded in 114
the vicinity of the evaporating surface because of frictional resistance. The air velocity parallel to 115
the evaporating surface increases from 0=V at 0=z (no-slip) asymptotically to ∞=VV at a 116
distance sufficiently far away from the surface. For fully laminar flow conditions, the thickness 117
of the boundary layer of retarded velocity (defined as ∞≤ VV 990. ) is inversely proportional to 118
the square root of the free-stream velocity (Rohsenow and Choi, 1961): 119
∞∝δ VV 1 [7] 120
Because the equations that describe laminar air flow parallel to a flat surface and 121
diffusion from a flat surface are analogous (Rohsenow and Choi, 1961), a similar notion of 122
concentration boundary layer holds near the evaporating surface. The vapor concentration profile 123
is illustrated in Fig. 1b. The vapor concentration decreases from an equilibrium value ( 0CC = ) at 124
0=z to a value determined by the free-stream humidity at sufficiently far distance. The 125
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
Page 8of 39
concentration boundary layer thickness ( Cδ ) is related to the velocity boundary layer thickness 126
by the Schmidt number, 127
D
Sca
a
V
C
⋅ρµ
=δδ
= [8] 128
where aµ and aρ are the viscosity and density of air, respectively. At 20 °C and 1 atm pressure, 129
the Schmidt number is approximately unity. In the remainder of this paper the subscripts in the 130
boundary layer thickness are dropped and CV δ=δ=δ . It is evident from [7] and [8] that the 131
concentration BLT ( δ ) is inversely related to the square root of the free-stream velocity ( ∞V ) 132
and can serve as a direct measure of the tunnel ventilation condition. In a subsequent subsection, 133
estimation of the BLT will provide further elaboration on the dependence of δ on ventilation 134
conditions. 135
Fig. 1. Schematic description of (a) air velocity and (b) vapor concentration profiles above a 136
free water surface 137
Boundary Conditions 138 The domain of the vapor diffusion equation [4] is the concentration boundary layer 139
introduced in the preceding subsection. The boundary condition on [4] corresponding to the 140
equilibrium vapor concentration at the evaporating surface ( 0=z ) is given by (using [2] and 141
[6]): 142
ρ
==TR
MPp
TRM
CC WW
Cs
W exp0 [9] 143
The second boundary condition is at the border of the concentration boundary layer δ=z , where 144
the vapor concentration is defined by the relative humidity ( h ) of the ambient air: 145
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
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hpTR
MCC s
W== ∞ [10] 146
If the boundary conditions change slowly, the evaporation rate can be considered to be at 147
steady state and the concentration gradient zC dd is constant throughout the boundary layer. 148
Then, the steady state vapor diffusion equation [4] under isothermal conditions is simplified to 149
δ−
⋅−=∞CCDJ vV
0 [11] 150
Note that the ratio vDδ is commonly referred to as aerodynamic resistance. The isothermal 151
vapor diffusion equation [11] is considered valid for modeling evaporation from tunnel surfaces 152
and free water. Fujimaki and Inoue (2003) found [11] (also known as the bulk transfer equation) 153
to be valid in laboratory evaporation experiments in which the ambient air velocity was on the 154
order of 1 m/s. All the variables of this model are directly related to physical conditions in the 155
tunnel, and all of them, except δ , can be independently determined from measured quantities. 156
The boundary-layer thickness (δ ) can be estimated by calibrating [11] against free water 157
evaporation data, as discussed in the next subsection. 158
Estimation of the Boundary-Layer Thickness 159 Apart from the capillary pressure at the evaporating surface, evaporation from free water 160
and that from a wet porous surface are thus far assumed to be identical processes. Therefore, a 161
controlled evaporation experiment from a still water surface can be used to estimate the vapor 162
concentration boundary layer thickness, which is also applicable to evaporation from wet tunnel 163
surfaces at similar ventilation conditions. Upon substitution of [1], [5], [9], and [10] in [11], and 164
noting that the capillary pressure of the free water surface is 0=CP , we arrive at a free-water 165
evaporation equation, 166
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
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δ−
⋅
+
+⋅
×−= −
hTR
Mc
bTTaT
PJ wV
115273
1010132815
5.
.. [12] 167
According to the isothermal assumption, T denotes the temperature of the evaporating surface 168
and the surrounding air. Assuming the change in conditions that affect evaporation rate is slow 169
compared to the time it takes to reach steady-state evaporation, [12] can be fitted to time-series 170
data of evaporation rate data, measured at known temperature, pressure, and relative humidity 171
conditions. The best-fit δ represents the boundary-layer thickness at the prevailing ventilation 172
condition. However, it should also be noted that uncertainties associated with the assumed 173
simplifications (including isothermal conditions, flat evaporating surface, and laminar airflow) 174
are lumped in this parameter. Thus, the boundary-layer thickness should be considered an 175
effective parameter. 176
Evaporation from Porous Surface 177 The surface of an unsaturated porous medium typically consists of solid (matrix of the 178
medium) and pore/fracture (liquid and gas) components, rendering the evaporating surface 179
heterogeneous with respect to vapor concentration, as illustrated in Fig. 2a. During seepage, 180
however, tunnel ceilings are usually covered with liquid films (e.g., Trautz and Wang, 2001), and 181
the vapor concentration could be considered locally homogeneous. For simplicity, we extend 182
this assumption of locally uniform distribution of vapor concentration to the entire tunnel Fig. 183
2b. The vapor concentration at any given location on the tunnel is assumed to be at capillary 184
equilibrium with the pores and fractures of the porous medium. The datum 0=z for the vapor 185
diffusion is set on the surface of the tunnel (as illustrated in Fig. 2b). Although this assumption is 186
likely to fail at very low saturations (when the liquid is scattered in a few fine pores and 187
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
Page 11of 39
fractures) it is expected to be of marginal consequence because the evaporation rate under such 188
conditions is very low. 189
Fig. 2. Evaporating surface area of a porous medium: (a) partitioning of the surface into non-190
evaporating solid and evaporating pores; (b) proposed approach of uniform gas-phase 191
surface. The dark shade denotes vapor in pores and/or fractures. 192
COUPLED SEEPAGE AND EVAPORATION 193 In a tunnel constructed in unsaturated formations, the flow velocity of water in the rock is 194
usually stagnated near the crown, resulting in elevated moisture (Philip et al., 1989b). Unlike 195
evaporation from ground surface, where infiltration opposes the evaporation flux, the condition 196
in tunnels is favorable for simultaneous occurrence of evaporation and seepage. Field tests that 197
exhibit simultaneous evaporation and seepage are described below. After field test descriptions, 198
we present a brief description of seepage modeling using the numerical simulators TOUGH2 199
(Pruess et al., 1999) and iTOUGH2 (Finsterle, 1999) and discuss implementation of evaporation 200
in these models. 201
Field Tests 202 The data reported in this paper were obtained from field tests and measurements 203
conducted at the proposed nuclear waste repository at Yucca Mountain currently under 204
investigation by the US Department of Energy (DOE). Air-injection tests were conducted to 205
characterize the permeability and small-scale heterogeneities of the formation, and liquid-release 206
tests were performed to study seepage phenomena. Relative humidity, temperature, and free-207
water evaporation were monitored at the test site to assess the evaporation conditions. Detailed 208
description of the site and tests conducted at the site are provided elsewhere (Birkholzer et al., 209
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
Page 12of 39
1999; Bodvarsson et al., 1999; Finsterle and Trautz, 2001; Finsterle et al., 2003; Trautz and 210
Wang, 2001; Trautz and Wang, 2002; Wang et al., 1999). This study is concerned with the lower 211
lithophysal welded tuff unit at Yucca Mountain, in which about 80% of the proposed repository 212
is expected to reside. This unit contains many small fractures (less than 1 m long) and is 213
interspersed with numerous lithophysal cavities (0.15 m–1 m in diameter). 214
In the lower lithophysal unit, an 800-m long drift (5 m in diameter) for enhanced 215
characterization of the repository block (ECRB) was excavated off the main Exploratory Studies 216
Facility (ESF) tunnel. Liquid-release and air-injection tests were systematically conducted in this 217
ECRB Cross Drift along boreholes drilled into the ceiling of the Cross Drift at regular intervals. 218
Similar tests were conducted in a short (approximately 15 m long) drift excavated off the Cross 219
Drift (niches). Schematic alignment of the tunnels is shown in Fig. 3a. This paper is concerned 220
with tests conducted at a Cross Drift borehole designated as LA#2 (Fig. 3b) and a short drift 221
known as Niche 5 (Fig. 3c). The tests and measurements conducted in the Cross Drift and Niche 222
5 are briefly described below. 223
Air-injection tests 224
The purpose of the air-injection tests was to estimate absolute permeability of the 225
formation as a basis for the stochastic generation of heterogeneous permeability fields. Short 226
sections of the boreholes (0.3 m in Niche 5, 1.8 m in Cross Drift) were isolated using an 227
inflatable packer system, and compressed air was injected. Air injection was terminated when 228
steady-state pressure was reached. Air-permeability values were derived from the steady-state 229
pressure data according to an analytical solution of LeCain (1995). Permeabilities determined 230
from air-injection tests were considered representative of the absolute permeability of the test 231
interval. 232
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
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Liquid-release Tests 233
Liquid release tests were conducted in boreholes drilled above tunnels to evaluate 234
seepage into waste emplacement drifts. The alignment of the boreholes and test intervals are 235
schematically shown in Fig. 3. The liquid release boreholes in the Cross Drift were 236
approximately 20 m long, drilled into the ceiling of the Cross Drift at a nominal inclination of 237
15° from the horizontal. Liquid release data from a borehole designated as LA#2 were used in 238
this study. The borehole was partitioned into three zones (designated as Zone 1, Zone 2, and 239
Zone 3) available for liquid release testing. The distances from the middle of the liquid-release 240
zones to the drift crown were 1.58 m, 2.84 m, and 4.10 m for Zone 1, Zone 2, and Zone 3, 241
respectively. The liquid release boreholes in Niche 5 were near horizontal. Of the six boreholes 242
available for tests, data from boreholes #4 and #5 were used in this study. The liquid release tests 243
were performed by injecting water into a test interval isolated by inflated rubber packers. Water 244
that seeped into the tunnels was captured and measured using automated recording devices. 245
Relative Humidity and Temperature Measurements 246
The Cross Drift was actively ventilated during regular working hours, thus the relative 247
humidity of the tunnel was usually low. To mitigate the effect of evaporation in the seepage 248
process, the seepage collection interval was guarded using curtains on both ends. Because Niche 249
5 was isolated from the actively ventilated Cross Drift by a bulkhead, the relative humidity was 250
relatively high. To aid in the estimation of evaporation during the liquid release tests, the relative 251
humidity and temperature of the air inside and outside of the curtains (for the Cross Drift) and in 252
front of and behind the bulkhead (for Niche 5) were monitored. 253
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
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The evaporation rate from still water was measured by monitoring the level (mass) of 254
water in evaporation pans placed within the space enclosed by the seepage capture tray and end 255
curtains (for the Cross Drift tests) and behind the bulkhead (for Niche 5). 256
Fig. 3. Schematic alignment of tunnels and boreholes: (a) parts of the Exploratory Studies 257
Facility (ESF) tunnel and Enhanced Characterization of the Repository Block (ECRB) 258
cross-drift; (b) liquid release test setup in the Cross Drift, including liquid release 259
intervals and liquid injection and seepage collection equipment; and (c) vertical section 260
of Niche 5 along with location of all the test boreholes. 261
TOUGH2/iTOUGH2 Seepage Model 262 A detailed description of the numerical models developed for flow in fractured formation 263
around a tunnel and associated seepage into the tunnel using TOUGH2/iTOUGH is given by 264
Finsterle et al (2003). A summary follows. 265
The TOUGH2 code is an integral finite difference simulator that represents unsaturated 266
flow at the scale of individual grids by Richards’ equation (Bear, 1972; Pruess et al., 1999) 267
( )
ρ+∇
µρ
=∂∂
ρφ gzPkSt Ce
div [13] 268
The appropriateness of using this continuum approach to simulate water flow through 269
unsaturated fractured rock was shown by Finsterle (2000). The effective permeability ( k ) and 270
capillary pressure ( CP ) are functions of liquid saturation as given by van Genuchten’s models 271
(1980) 272
( ) 2121 11
−−=
mmeea SSkk
// [14] 273
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
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[ ] mmeC SP −− −α−=11 11 / [15] 274
where ak is the absolute permeability, α1 and m are fitting parameters with 0>α and 275
10 zq ) occurs only when the following condition is satisfied: 291
zgPC ∆ρ>−∗ [17] 292
where ∗CP is the threshold capillary pressure at the last node adjacent to the opening. The critical 293
capillary pressure zgPC ∆ρ−=∗ depends on the grid size or nodal distance of the numerical 294
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
Page 16of 39
model. According to [17], the tunnel surface does not need to be fully saturated for seepage to 295
commence as in the case of unfractured homogeneous porous media (Philip et al., 1989b). 296
Fig. 4. Schematic description of the seepage and evaporation connections between nodes that 297
represent the rock of the tunnel wall and the tunnel. 298
Implementation of Evaporation in TOUGH2 299 While seepage occurs only when the critical condition given in [17] is satisfied, vapor 300
flow from/to tunnel walls to/from tunnel air occurs as long as there is vapor pressure 301
disequilibrium between them. Coupling of the seepage and evaporation processes is illustrated in 302
Fig. 4. Mass-transfer rate of water, including seepage, is represented in TOUGH2 by equations 303
similar to [16], where the driving force is pressure gradient. To incorporate evaporation into the 304
existing model without significant changes to the governing flow equations, we must rewrite the 305
concentration-gradient dependent diffusion equation [11] in the form of equation [16]. Noting 306
that the connection length z∆ denotes the vapor concentration boundary layer thickness δ , the 307
equivalent evaporative permeability can be written as 308
−
−ρµ
=∞
∞
CCveq
PPCCDk
0
0 [18] 309
where the variables with a superscript of 0 correspond to the tunnel wall and those with a 310
superscript of ∞ denote the tunnel air. The capillary pressure of the tunnel ∞CP is equivalent to 311
the relative humidity [3] of the tunnel, as described by Kelvin’s equation [2]. The vapor 312
concentrations are computed according to [11] and [12]. Equation [18] was implemented in 313
TOUGH2 as a special evaporation connection. When the conditions for both evaporation and 314
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
Page 17of 39
seepage permit, the total mass flow from the tunnel wall to the tunnel is considered as the sum of 315
both. 316
Numerical Meshes 317 Different numerical models were constructed to simulate liquid-release tests and seepage 318
into the underground openings at different test locations. Three-dimensional meshes of the test 319
sites were generated with grid sizes of 0.3 m × 0.1 m × 0.1 m for the Cross Drift and 0.1 m × 320
0.1 m × 0.1 m for Niche 5 (see Fig. 5). For the Cross Drift meshes, a circular cylindrical tunnel 321
of 5 m diameter was removed from the center of the mesh to represent the tunnel. Only one half 322
of the symmetric mesh was used in the simulations to save computational load. For the Niche 5 323
meshes, surveyed niche geometry was removed from the numerical mesh to replicate the test 324
sites. The liquid-release boreholes are indicated in Fig. 5 by bold black lines, and the white 325
sections at the middle of the boreholes represent the injection intervals. The Cross Drift borehole 326
is inclined while the Niche 5 boreholes are parallel to the centerline of the niche. The Cross Drift 327
mesh in Fig. 5a represents the Zone 2 test interval. In Fig. 5b and Fig. 5c, boreholes #4 and #5 328
are revealed, respectively (see also Fig. 3c). Notice that the injection intervals in boreholes #4 329
and #5 are located at 3–3.5 m and 8.5–8.8 m, respectively, from the borehole collars; hence, the 330
respective tunnel outlines are different. 331
Fig. 5. Numerical meshes of (a) Niche 5 with borehole #4, (b) Niche 5 with borehole #5, and 332
(c) the Cross Drift, along with a typical realization of the correlated stochastic 333
permeability field. Bold black lines denote the liquid-release boreholes, and the white 334
section in the middle of the boreholes is the injection interval. 335
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
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The spatial structure of the Niche 5 permeability data was analyzed using the GSLIB 336
module GAMV3 (Deutsch and Journel, 1992) and a spherical semivariogram was fitted to the 337
resulting variogram. Because only six permeability data were available from the Cross Drift, 338
assumed spherical variogram parameters were used. Recall that the permeability of the Cross 339
Drift was measured on 1.8 m long intervals of the boreholes, and the standard deviation of the 340
measured data was 0.21. The variability of the permeability on the scale of the 0.3 m long 341
gridblock was expected to be greater than the measurement interval. For the purpose of 342
generating a heterogeneous field, the permeability was taken to be log-normally distributed with 343
a variance (sill) value of 1 order of magnitude. Computed and prescribed geostatistical 344
parameters (Table 1) were used to generate spatially correlated permeability fields, using the 345
sequential indicator simulation (SISIM) module of the GSLIB (Deutsch and Journel, 1992). 346
Multiple realizations of the permeability field were generated and mapped to the numerical 347
meshes. Representative permeability field realizations for the Cross Drift and Niche 5 are shown 348
in Fig. 5. 349
Table 1. Mean, standard deviation, and correlation length of log-permeability data collected in 350
the Cross Drift and Niche 5. The values in parentheses are prescribed values because the 351
number of measurements was not adequate to compute the respective parameters. 352
Spherical Variogram Location n Mean log (k) [m2]
Std. Dev. [m2] Sill Value
[log(k)2] Correlation length
[m] Nugget effect
[log(k)2]
Niche 5 61 -10.95 1.31 1.81 0.91 0.02
Cross Drift 6 -10.73 0.21 1.0 0.2 -
353
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
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The tunnels were represented in the seepage models by two types of overlapping 354
gridblocks, one corresponding to seepage and the other to evaporation. The seepage gridblocks 355
were assigned a zero capillary pressure, whereas the evaporation gridblocks were assigned a 356
capillary pressure and vapor concentration corresponding to the tunnel relative humidity of the 357
tunnel, as given by [2] and [3]. No-flow boundary conditions are specified at the left, right, front, 358
and back sides of the model. A free-drainage boundary condition is applied at the bottom to 359
prevent an unphysical capillary boundary effect. 360
RESULTS AND DISCUSSIONS 361
Evaporation Boundary Layer 362 The evaporation data collected in Niche 5 were used to calibrate the evaporation model. 363
The data were grouped into three classes based on airflow velocity (ventilation): (1) inside Niche 364
5 without ventilation; (2) outside Niche 5 with active ventilation; and (3) outside Niche 5 without 365
active ventilation, the regime usually encountered during nights and weekends. In Fig. 6, the 366
measured relative humidity, and temperature, and evaporation rates from still water are plotted. 367
The evaporation model [12] was fitted to the measured data by adjusting the boundary layer 368
thickness. The best-fit estimates of the boundary layer thickness are listed in Table 2. 369
Fig. 6. Temperature, humidity, and evaporation rate data, along with model fit of the 370
evaporation data for inside and outside of Niche 5. 371
In agreement with the theoretical assessment (Equation [7]), the estimated δ showed an 372
inverse relationship with the ventilation conditions. Inside Niche 5, the air was the calmest 373
because it was isolated from the Cross Drift by a bulkhead (see Fig. 3). As a result, the thickest 374
boundary layer (20 mm) was obtained inside Niche 5. Fig. 6 shows that the relative humidity 375
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
Page 20of 39
outside Niche 5 increases at nights and during weekends when active tunnel ventilation is turned 376
off. However, this increase in relative humidity is insufficient to explain the observed decrease in 377
evaporation. Therefore, as shown in Fig. 6, reduced air ventilation during nights and weekends is 378
also accompanied by an increase in the thickness of the boundary layer. The estimated boundary-379
layer-thickness values and Equation [7] suggest that the air velocity outside Niche 5 is higher 380
than the inside by factors of 7 (without active ventilation) and 16 (with active ventilation). These 381
results confirm the applicability of Equation [12] to describe the effects of humidity, 382
temperature, and ventilation on evaporation rate. 383
Table 2. Summary of estimated boundary layer thickness for Niche 5 and their application. 384
Location of Experiment δ (mm) Used For Simulation of Liquid-Release Tests in
Inside Niche 5 20.0 Niche 5
Outside Niche 5, ventilation off 7.5 Cross Drift (with end curtains)
Outside Niche 5, ventilation on 5.0 Not used
385
Coupled Seepage and Evaporation 386 In this section, simulations of coupled seepage and evaporation are compared with 387
measured seepage rate data. The software iTOUGH2 (Finsterle, 1999) was used to match the 388
simulated seepage rate with the measured values by adjusting the free capillary strength 389
parameter ( α1 ) (Finsterle et al., 2003). The corresponding evaporation rate from the tunnel 390
walls simulated using the tunnel relative humidity and calibrated boundary layer thickness. 391
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
Page 21of 39
Niche 5 392
Here, two different data sets from liquid release tests conducted in boreholes #4 (October, 393
2002) and #5 (July 2002) are compared with the Niche 5 seepage models. The liquid release rate, 394
seepage rate, and relative humidity data as well as modeled liquid release rate and fitted seepage 395
rate are shown in Fig. 7. The best-fit α1 values were 223671± Pa and 339740 ± Pa for 396
boreholes #4 (30 inversions) and #5 (24 inversions), respectively. The measured seepage rates 397
attained a steady-state flow rate after several days. Because the early-time transient data are 398
biased by storage (e.g., in lithophysal cavities and matrix) and/or fast flow paths connecting the 399
injection interval to the tunnel ceilings, the model was fitted to the late-time steady state data. In 400
the simulations, the relative humidity was kept constant at 0.85 to match with the lowest steady-401
conditions observed during the borehole #4 tests. 402
Fig. 7. Calibration of seepage-rate data from liquid-release tests conducted in Niche 5. 403
Calculated seepage rate curves show only one of the multiple inversions. 404
To quantify the impact of evaporation on seepage over the observed high relative 405
humidity range (0.85–0.99), the calibrated seepage model of borehole #4 was used to simulate 406
seepage and evaporation at relative humidity values of 0.85, 0.95, and 0.99. The resulting steady 407
state seepage and evaporation rates (on Day 10) are plotted as percentages of the liquid release 408
rate in Fig. 8. At a relative humidity of 0.85, the evaporation rate from the entire niche wall 409
surface and the seepage rate are comparable in magnitude. As the relative humidity was 410
increased, the steady-state evaporation rate showed a drastic decrease, while the corresponding 411
seepage rate increased only slightly. Thus, at these high relative humidity conditions, the main 412
impact of evaporation is on the quantity of liquid diverted around the tunnel. 413
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
Page 22of 39
Fig. 8. Effect of high relative humidity on evaporation and seepage rates. 414
ECRB Cross Drift 415
In this subsection, two different data sets from liquid release tests conducted in borehole 416
LA2, Zone 2 and Zone 3, are compared with the ECRB Cross Drift seepage model. The liquid 417
release rate, seepage rate, and relative humidity data, as well as modeled liquid-release rates and 418
fitted seepage rates, are plotted in Fig. 9. The best-fit capillary-strength parameter α/1 were 557 419
± 56 Pa for zone 2 and 535 ± 58 Pa for zone 3, based on 21 and 19 inversions, respectively. Note 420
that both of the liquid-release tests were conducted concurrently. The measured and simulated 421
seepage rate fluctuations were strongly correlated to the drastic changes in relative humidity 422
(hence, evaporation). The model captured this evaporation effect satisfactorily, tracking 423
increases in measured seepage rates as relative humidity increases and vice versa. 424
Fig. 9. Calibration of seepage-rate data from liquid-release tests conducted in the ECRB Cross 425
Drift. Calculated seepage rate curves show only one of the multiple inversions. 426
The interplay between relative humidity fluctuation and dynamics of flow and ceiling 427
wetness at different times during the test in Zone 2 are visualized in Fig. 10. During this test, the 428
liquid release rate was relatively stable (steadily increasing from 31 mL/min on Day 0 to 34 429
mL/min on Day 34). However, the relative humidity fluctuated between 30% and 90% during 430
this period. Fig. 10 shows snapshots of the liquid saturation distribution on Days 0, 10, 20, and 431
30. Just before the test began, the drift wall has dried out because of the low relative humidity in 432
the drift. The liquid saturation at this time was in equilibrium was the assumed background 433
percolation flux of 2 mm/yr. On day 10 day of injection (relative humidity ~ 70%), water 434
reached the crown of the drift, seepage has started, water was being diverted around the drift, and 435
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
Page 23of 39
wet plume has reached approximately to the elevation of the spring line. After 20 days, however, 436
the plume has shrunk significantly because of reduced humidity (approximately 12%) and 437
increased evaporation. Moreover, the seepage rate and seepage locations (indicated by inverted 438
triangles) have decreased. Before the 30-day time mark, the relative humidity rose up to 439
approximately 80%; thus, the evaporation rate was reduced, the wet plume grew, and seepage 440
rate and number of seeps increased. In general, despite the high liquid release rate, the flow 441
regime remained unsaturated. The liquid saturation was highest near the drift crown, which 442
induces a capillary pressure gradient that promoted flow diversion around the drift (capillary 443
barrier effect). Seepage and evaporation removed water from the formation as water flows 444
around the drift, limiting the spread of the wetted region on the drift wall. 445
Fig. 10. Liquid saturation distribution simulated with model calibrated against seepage-rate data 446
from liquid-release tests conducted in the Cross Drift borehole LA#2, Zone 2 at 0, 10, 447
20, and 30 days after the start of the liquid release tests. Note the correlation of tunnel 448
wall wetness to tunnel relative humidity. 449
SUMMARY AND CONCLUSIONS 450 In this paper, we (1) estimated the evaporative boundary-layer thickness by calibrating a 451
semi-physical evaporation model, which considers isothermal vapor diffusion; (2) calibrated a 452
heterogeneous fracture-continuum model against seepage-rate data; and (3) tested the effect of 453
evaporation on seepage predictions. The major conclusions of this study are listed below: 454
1. The simplified vapor-diffusion approach of modeling evaporation was found to be effective 455
in capturing the roles of the important environmental conditions that affect evaporation – 456
namely, relative humidity, temperature, and ventilation. Calibrated thicknesses of the 457
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
Page 24of 39
evaporation boundary layer were obtained for three ventilation conditions representing the 458
conditions at the liquid-release test sites at Yucca Mountain. 459
2. We found that evaporation reduces seepage significantly in tests conducted under 460
ventilated conditions. Therefore, it is important to account for evaporation effects when 461
calibrating a seepage process model against liquid-release-test data collected under 462
ventilated conditions. In contrast, the impact of evaporation on seepage rate was minimal in 463
closed-off niches, where relative humidity values were generally high. Thus, when using 464
data obtained from closed-off and/or artificially humidified niches, ignoring the effect of 465
evaporation is expected to introduce little error in the estimation of seepage-relevant 466
parameters. 467
3. The classification of ventilation regimes is based on crude assessment of the tunnel 468
environment. Bearing of external wind velocity variations (note that the Cross Drift is 469
connected to the air outside the ESF) was not accounted for. The matching between 470
measured evaporation rate and model predictions can be improved if accurate measurement 471
of air velocity in the tunnels was made. 472
ACKNOWLEDGMENT 473 We thank Jens Birkholzer and Guomin Li for their thorough reviews and insightful 474
comments. This work was supported by the Director, Office of Civilian Radioactive Waste 475
Management, U.S. Department of Energy, through Memorandum Purchase Order 476
EA9013MC5X between Bechtel SAIC Company, LLC, and the Ernest Orlando Lawrence 477
Berkeley National Laboratory (Berkeley Lab). The support is provided to Berkeley Lab through 478
the U.S. Department of Energy Contract No. DE-AC03-76SF00098. 479
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
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480
481
482
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
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REFERENCES 482 Bear, J., 1972. Dynamics of fluids in porous media Elsevier, New York, New York. 483
Birkholzer, J., G.M. Li, C.F. Tsang, and Y. Tsang, 1999. Modeling studies and analysis of 484
seepage into drifts at Yucca Mountain. Journal of Contaminant Hydrology 38:349-384. 485
Bodvarsson, G.S., W. Boyle, R. Patterson, and D. Williams, 1999. Overview of scientific 486
investigations at Yucca Mountain - the potential repository for high-level nuclear waste. 487
Journal of Contaminant Hydrology 38:3-24. 488
Deutsch, C.V., and A.G. Journel, 1992. Gslib: Geostatistical software library and user's guide 489
Oxford University Press, New York, New York. 490
Finsterle, S. 1999. Itough2 user’s guide Report No. LBNL-40040. Lawrence Berkeley National 491
Laboratory. 492
Finsterle, S., 2000. Using the continuum approach to model unsaturated flow in fractured rock. 493
Water Resources Research 36:2055-2066. 494
Finsterle, S., and R.C. Trautz, 2001. Numerical modeling of seepage into underground openings. 495
Mining Engineering 53:52-56. 496
Finsterle, S., C.F. Ahlers, R.C. Trautz, and P.J. Cook, 2003. Inverse and predictive modeling of 497
seepage into underground openings. Journal of Contaminant Hydrology 62-63:89-109. 498
Fujimaki, H., and M. Inoue, 2003. A transient evaporation method for determining soil hydraulic 499
properties at low pressure. Vadose Zone J 2:400-408. 500
Ho, C.K., 1997. Evaporation of pendant water droplets in fractures. Water Resources Research 501
33:2665-2671. 502
Knight, J.H., J.R. Philip, and R.T. Waechter, 1989. The seepage exclusion problem for spherical 503
cavities. Water Resources Research 25:29-37. 504
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
Page 27of 39
LeCain, G.D. 1995. Pneumatic testing in 45-degree-inclined boreholes in ash-flow tuff near 505
superior, arizona Water-Resources Investigations Report 95-4073. U.S. Geological Survey, 506
Denver, Colorado. 507
Li, G.M., and C.-F. Tsang, 2003. Seepage into drifts with mechanical degradation. Journal of 508
Contaminant Hydrology 62:157-172. 509
Murray, F.W., 1966. On the computation of saturation vapor pressure. J. Appl. Meteor. 6:204. 510
Or, D., and T.A. Ghezzehei, 2000. Dripping into subterranean cavities from unsaturated fractures 511
under evaporative conditions. Water Resources Research 36:381-393. 512
Philip, J.R., 1989a. Asymptotic solutions of the seepage exclusion problem for elliptic-513
cylindrical, spheroidal, and strip-shaped and disc- shaped cavities. Water Resources 514
Research 25:1531-1540. 515
Philip, J.R., 1989b. The seepage exclusion problem for sloping cylindrical cavities. Water 516
Resources Research 25:1447-1448. 517
Philip, J.R., J.H. Knight, and R.T. Waechter, 1989a. The seepage exclusion problem for 518
parabolic and paraboloidal cavities. Water Resources Research 25:605-618. 519
Philip, J.R., J.H. Knight, and R.T. Waechter, 1989b. Unsaturated seepage and subterranean holes 520
- conspectus, and exclusion problem for circular cylindrical cavities. Water Resources 521
Research 25:16-28. 522
Pruess, K., C. Oldenburg, and G. Moridis. 1999. Tough2 user's guide, version 2.0 LBNL-43134. 523
Lawrence Berkeley National Laboratory, Berkeley, Calif. 524
Rohsenow, W.M., and H. Choi, 1961. Heat, mass and momentum transfer Prentice-Hall Inc., 525
Englewood Cliffs, New Jersey. 526
Trautz, R.C., and J.S.Y. Wang, 2001. Evaluation of seepage into an underground opening using 527
small- scale field experiments, yucca mountain, nevada. Mining Engineering 53:41-44. 528
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
Page 28of 39
Trautz, R.C., and J.S.Y. Wang, 2002. Seepage into an underground opening constructed in 529
unsaturated fractured rock under evaporative conditions. Water Resources Research 530
38:1188. 531
van Genuchten, M.T., 1980. A closed-form equation for predicting the hydraulic conductivity of 532
unsaturated soils. Soil Science Society of America Journal 44:892-898. 533
Wang, J.S.Y., R.C. Trautz, P.J. Cook, S. Finsterle, A.L. James, and J. Birkholzer, 1999. Field 534
tests and model analyses of seepage into drift. Journal of Contaminant Hydrology 38:323-535
347. 536
Zhang, J.T., and B.X. Wang, 2002. Effect of capillarity at liquid-vapor interface on phase change 537
without surfactant. International Journal of Heat & Mass Transfer 45:2689-2694. 538
Zhang, J.T., B.X. Wang, and X.F. Peng, 2001. Thermodynamic aspect of the shift of concave 539
liquid-vapor interfacial phase equilibrium temperature and its effect on bubble formation. 540
International Journal of Heat and Mass Transfer 44:1681-1686. 541
542
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Figures
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
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Fig. 1. Schematic description of (a) air velocity and (b) vapor concentration profiles above a free water surface
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
Page 31of 39
z=0
z=0
Solid
Pore/Fracture
Evaporation(a)
(b)
Fig. 2. Evaporating surface area of a porous medium: (a) partitioning of the surface into non-evaporating solid and evaporating pores; (b) proposed approach of uniform gas-phase surface.
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
Page 32of 39
Fig. 3. Schematic alignment of tunnels and boreholes: (a) parts of the Exploratory Studies Facility (ESF) tunnel and Enhanced Characterization of the Repository Block (ECRB) cross-drift; (b) liquid release test setup in the Cross Drift, including liquid release intervals and liquid injection and seepage collection equipment; and (c) vertical section of Niche 5 along with location of all the test boreholes.
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
Page 33of 39
Fig. 4. Schematic description of the seepage and evaporation connections between nodes that represent the rock of the tunnel wall and the tunnel.
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
Page 34of 39
Fig. 5. Numerical meshes of (a) Niche 5 with borehole #4, (b) Niche 5 with borehole #5, and (c) the Cross Drift, along with a typical realization of the correlated stochastic permeability field. Bold black lines denote the liquid-release boreholes, and the white section in the middle of the boreholes is the injection interval.
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
Page 35of 39
Day of Year 2002
130 137 144 151
Evap
. Rat
e (m
m/d
ay)
0.0
0.5
1.0
1.5
4.0
8.0
12.0
Measured Model
Rel
. Hum
idity
(%)
0
25
50
75
100
Inside Niche 5
Tem
pera
ture
(°C
)
24
26
28
Day of Year 2002
130 137 144 151
Outside Niche 5
Wee
kend
Nig
hts
Fig. 6. Temperature, humidity, and evaporation rate data, along with model fit of the evaporation data
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
Page 36of 39
Days
0 2 4 6 8 10 12
Seep
age
Rat
e (m
l/min
)
0
1
2
3
4
5
6
7
Niche 5, Borehole #5
Days
0 2 4 6 8 10 12 14
MeasuredCalculated
Rel
ativ
e H
umid
ity (%
)
0
20
40
60
80
100
MeasuredModeled
Niche 5, Borehole #4
Rel
ease
Rat
e (m
l/min
)
0
5
10
15
20
25
MeasuredModeled
Fitted Range
Fitted Range
Fig. 7. Calibration of seepage-rate data from liquid-release tests conducted in Niche 5. Calculated seepage rate curves show only one of the multiple inversions.
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
Page 37of 39
Relative Humidity (%)
80 85 90 95 100
Flow
Rat
e (m
l/min
)
0.0
0.5
1.0
1.5
2.0
Evaporation
Seepage
Fig. 8. Effect of high relative humidity on evaporation and seepage rates.
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
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LA#2 Zone 2
Days
0 5 10 15 20 25 30
LA#2 Zone 3
Rel
ease
Rat
e (m
l/min
)
0
10
20
30
40
50
60
MeasuredModeled
Days
0 5 10 15 20 25 30
Seep
age
Rat
e (m
l/min
)
0
1
2
3
4
5
6
7
8
MeasuredCalculated
Rel
ativ
e H
umid
ity (%
)
0
20
40
60
80
100
Measured & Modeled
Fig. 9. Calibration of seepage-rate data from liquid-release tests conducted in the ECRB Cross Drift. Calculated seepage rate curves show only one of the multiple inversions.
MODELING COUPLED EVAPORATION AND SEEPAGE IN VENTILLATED TUNNELS
Page 39of 39
Fig. 10. Liquid saturation distribution simulated with model calibrated against seepage-rate data from liquid-release tests conducted in the Cross Drift borehole LA#2, Zone 2 at 0, 10, 20, and 30 days after the start of the liquid release tests. Note the correlation of tunnel wall wetness to tunnel relative humidity.
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